Question

The following is an arithmetic sequence that has 10 numbers LaTeX: 1,\ a_2, \ a_3, \ a_4, \ \cdots,\ a_{10}.1 , a 2 , a 3 , a 4 , ⋯ , a 10 . If these 10 numbers add up to 100, what is the second number LaTeX: a_2a 2?

Answer 1

`a_2=3`

Explanation:

The arithmetic sequence is given as:
`1,\ a_2, \ a_3, \ a_4, \ \cdots,\ a_(10)`

We are told that the 10 numbers add up to 100.

`S_n=(n)/(2)(a_1+l)\\ $Where: \\n=number of terms\\l=last term\\a_1$=first term`

`S_(10)=100\\100=(10)/(2)(1+l)\\100=5(1+l)\\$Divide both sides by 5$\\20=1+l\\$Last term, $l=20-1=19`

We know that the nth term of an arithmetic sequence

`l=a_1+(n-1)d\\19=1+(10-1)d\\19=1+9d\\9d=19-1\\9d=18\\d=2`

Therefore, the second number

`a_2=a_1+2\\=1+2\\a_2=3`